Finite Group Databasebeta

← #18010107

Subgroups — #18010107

Order 4736.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558538C211yesmaximal, characteristic, complemented
2D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6C2×#10596953—21no—
7C2×D37⋊C8—21no—
8#11924603—21no—
9#11924603C2212yes—
10#11924603C2212yes—
11C4⋊#64438—21no—
12C2×#10596962—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924511C411yescharacteristic
17#11924509—21no—
18#11924507C411yescharacteristic
19C4×D148C411yescharacteristic
20C4×C22⋊D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C22×C4×C37—21no—
25C2×C22⋊D37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28#10596962—42no—
29#10596962—42no—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37C2×C411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×Dic74—21no—
37C2×#64438—22no—
38C2×#64438—22no—
39#10596953—42no—
40D37⋊C8—42no—
41C4⋊C4×C37C2×C411yescharacteristic
42C22⋊C4×C37—21no—
43C42×C37C2×C411yescharacteristic
44C22⋊Dic37—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37C2×C411yescharacteristic
48#10596936—21no—
49C4×Dic37D411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37C2311yescharacteristic
52C23×C37—21no—
53C22×D37—21no—
54C22×D37C22⋊C411yescharacteristic
55D4×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37—42no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C22⋊D37—42no—
62C22⋊D37—41no—
63C22⋊D37—41no—
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37—21no—
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69C2×Dic37C2×D411yescharacteristic
70D148—41no—
71D148—42no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—41no—
75C4×D37—42no—
76C4×D37D812yes—
77C4×D37SD1612yes—
78Dic74—41no—
79Dic74—41no—
80#64438—42no—
81#64438—42no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37#10212yes—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—41no—
95C4×C37#10212yes—
96Dic37—21no—
97Dic37—41no—
98Dic37C2×D811yescharacteristic
99Dic37C2×SD1611yescharacteristic
100Dic37AGL(1,ℤ/8)11yescharacteristic
101Dic37#13711yescharacteristic
102#1547—371nomaximal, Sylow
103C2×C37—81no—
104C2×C37#41311yescharacteristic
105C2×C37C2×#10211yescharacteristic
106C2×C37#41711yescharacteristic
107D37—22no—
108D37—81no—
109#532—371no—
110#423—371no—
111C2×C4⋊C8—371no—
112#332—372no—
113#331—372no—
114C37#154711yescharacteristic, complemented, Sylow
115C2×#41—741no—
116C2×M16—741no—
117C22×C8—741no—
118C4⋊Q8—371no—
119#127—371no—
120#124—741no—
121#121—371no—
122#121—371no—
123#121—741no—
124C4×D4—371no—
125C4×D4—741no—
126C4×D4#386611yescharacteristic
127C2×C42—371no—
128C4⋊C8—372no—
129C4⋊C8—372no—
130C4⋊C8—741no—
131C4⋊C8—741no—
132#41—1482no—
133#41—1482no—
134C2×Q8—741no—
135C2×D4—371no—
136C2×D4—741no—
137C2×D4—741no—
138C2×D4—741no—
139C2×D4—741no—
140C2×D4C2×#386611yescharacteristic
141C22×C4—21no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—741no—
146M16—1482no—
147C2×C8—742no—
148C2×C8—742no—
149C2×C8—1482no—
150C4⋊C4—371no—
151C4⋊C4—741no—
152C4⋊C4C2×#386611yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42C2×#386611yescharacteristic
161C23—21no—
162C23—371no—
163C23—741no—
164Q8—1481no—
165Q8—1481no—
166D4—41no—
167D4—1481no—
168D4—1482no—
169D4—1481no—
170D4—1481no—
171D4—1481no—
172D4—1481no—
173D4—1482no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—372no—
179C2×C4—372no—
180C2×C4—371no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1482no—
186C2×C4C22⋊#386611yescharacteristic
187C2×C4C22⋊#386611yescharacteristic
188C2×C4C22×#386611yescharacteristic
189C8—1482no—
190C8—1482no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—372no—
195C22—741no—
196C22—741no—
197C22—1481no—
198C22—1481no—
199C22—1481no—
200C22C2×C22⋊#386611yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—371no—
205C4—371no—
206C4—371no—
207C4—371no—
208C4—741no—
209C4—1481no—
210C4#1192459812yes—
211C2—81no—
212C2—2961no—
213C2—742no—
214C2#1455851911yescharacteristic
215C2C2×#1192459811yescharacteristic
216C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC4×Dic37C23
hypercenterC4×D4#3866
hypocenterC37#1547
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558538C2semidirect
2. D37⋊(C4⋊C8)C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
114. C37#1547semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145585382
D37⋊(C4⋊C8)2
#145583922
#145583912
#145580802
#154737